Events

• Online Kolchin Seminar in Differential Algebra

• Algebraic theory of differential and difference equations

• Galois differential theories and transcendence

See here for videos of some of my talks.

Publications

• On the proalgebraic fundamental group of topological spaces and amalgamated products of affine group schemes, with Ch. Deninger, to appear in a Proceedings volume in honor of Massimo Bertolini's 60th Birthday, Springer Proceedings in Mathematics & Statistics,  ArXiv:2306.03296

• Regular singular differential equations and free proalgebraic groups, Bulletin of the London Mathematical Society, link, ArXiv:2209.01764

• Étale difference algebraic groups, Annales de l'Institut Fourier, link, ArXiv:2108.04544

• A remark on torsors under affine group schemes, Transformation Groups, link, ArXiv:2203.16115

• Algebraic independence and linear difference equations, with B. Adamczewski, Th. Dreyfus, Ch. Hardouin, Journal of the European Mathematical Society 26(5), 1899-1932, 2024, link, ArXiv:2010.09266

• Subgroups of free proalgebraic groups and Matzat's conjecture for function fields, Israel Journal of Mathematics 253, 841-863, 2023, link, ArXiv:2102.02553

• Difference Galois theory and dynamics, with I. Tomašić, Advances in Mathematics 402, 2022, link, ArXiv:2106.05334

• Algebraic groups as difference Galois groups of linear differential equations, with A. Bachmayr, Journal of Pure and Applied Algebra 226(2), 2022, link, ArXiv:1912.01284

• Torsors for difference algebraic groups, with A. Bachmayr, Communications in Contemporary Mathematics 24(9), 2022,  link,  ArXiv:1607.07035 

• Expansive dynamics on profinite groups, Fundamenta Mathematicae 256, 77-112, 2022, link, ArXiv:2008.00755

• Finiteness properties of affine difference algebraic groups, International Mathematics Research Notices 2022(1), 506-555, 2022, link,  ArXiv:1405.6603

• The differential Galois group of the rational function field, with A. Bachmayr, D. Harbater,  J. Hartmann, Advances in Mathematics 381, 2021, link, ArXiv:2004.05906

• Almost-simple affine difference algebraic groups, Mathematische Zeitschrift 299, 473-526, 2021, link, ArXiv:2007.07137

• On the dimension of systems of algebraic difference equations, Advances in Applied Mathematics 123, 2021, link, ArXiv:2004.01596

• Free differential Galois groups, with A. Bachmayr, D. Harbater and J. Hartmann, Transactions of the American Mathematical Society 374(6), 4293-4308, 2021, link, ArXiv:1904.07806

• Model theory of proalgebraic groups, with Anand Pillay, Transactions of the American Mathematical Society 374(3), 2225-2267, 2021, link, ArXiv:1908.10064

• Solving difference equations in sequences: Universality and Undecidability, with G. Pogudin and T. Scanlon, Forum of Mathematics, Sigma, Volume 8, e33, 1-30, 2020, link, ArXiv:1909.03239

• Free proalgebraic groups, Épijournal de Géométrie Algébrique, Volume 4, Article no.1, 1-36, 2020, link, ArXiv:1904.07455

• Picard-Vessiot extensions inside the ring of sequences, Appendix to The Dynamical Mordell-Lang Conjecture for skew-linear self-maps by D. Ghioca and J. Xie, International Mathematics Research Notices, Issue 21, 7433-7453, 2020, link, ArXiv:1803.03871

• Strongly étale difference algebras and Babbitt's decomposition, with I. Tomašić, Journal of Algebra 504, 10-38, 2018, link, ArXiv:1405.6603 

• Differential embedding problems over complex function fields, with A. Bachmayr, D. Harbater, J. Hartmann , Documenta Mathematica 23, 241-291, 2018, link, ArXiv:1610.09336 

• Tannakian categories with semigroup actions, with A. Ovchinnikov, Canadian Journal of Mathematics 69 (3), 687-720, 2017, link, ArXiv:1403.3850 

• Difference algebraic relations among solutions of linear differential equations, with L. Di Vizio and Ch. Hardouin, Journal of the Institute of Mathematics of Jussieu 16 (1), 59-119, 2017 link, ArXiv:1310.1289 

• σ-Galois theory of linear difference equations, with A. Ovchinnikov, International Mathematics Research Notices 2015 (12), 3962-4018 link, ArXiv:1304.2649 

• Skolem-Mahler-Lech type theorems and Picard-Vessiot theory, Journal of the European Mathematical Society, Vol. 17, Issue 3, 523-533, 2015, link, ArXiv:1203.1449 

• Difference Galois theory of linear differential equations, with L. Di Vizio and Ch. Hardouin, Advances in Mathematics 260, 1-58, 2014, link, ArXiv:1302.7198 

• An intrinsic characterization of Picard-Vessiot extensions, Journal of Algebra 408, 183-188, 2014, link, ArXiv:1205.1726 

• Software for Discussing Parametric Polynomial Systems: The Gröbner Cover, with A. Montes, In: Hong H., Yap C. (eds) Mathematical Software ICMS 2014. Lecture Notes in Computer Science, vol 8592, 2014, link 

• A Chevalley theorem for difference equations, Mathematische Annalen, Vol. 354, Issue 4, 1369-1396, 2012, link, ArXiv:1010.5066 

• Existence of ∂-parameterized Picard-Vessiot extensions over fields with algebraically closed constants, Journal of Algebra 361, 163-171, 2012, link, ArXiv:1104.3514 

• On the Galois theory of strongly normal differential and difference extensions, Séminaires et Congrès 27, 221-240, 2012, link 

• Gröbner bases for polynomial systems with parameters, with A. Montes, Journal of Symbolic Computation, Vol. 45, Issue 12, 1391-1425, 2010, link 

• Leakage quantification of cryptographic operations, with D. Biswas and F. Kerschbaum, In OTM Conferences (1) 2010: 685-700, link 

• Gröbner bases for families of affine or projective schemes, Journal of Symbolic Computation, Vol. 42, Issue 8, 803-834, 2007, link, ArXiv:0608019 

• On the dimension of coinvariants of permutation representations, with L. Smith, Monatshefte für Mathematik 151, no. 1, 75-81, 2006, link 

• On invariant relations between zeros of polynomials, with K. Girstmair and F. Pauer, Communications in Algebra 33, no. 7, 2157-2166, 2005, link 

Preprints

• Differential Galois groups, specializations and Matzat's conjecture, with R. Feng, ArXiv:2209.01581

Theses

• Affine difference algebraic groups, Habilitation thesis, RWTH Aachen University, 2015, pdf

• Geometric difference Galois theory, PhD thesis, University of Heidelberg, 2010, link, pdf

Lecture notes

• Differential Galois theory, an introduction to the Galois theory of linear differential equations

• Algebraic difference equations, an introduction to difference algebra 

Meetings (I co-organized)

• DART XI (London, May 2023)

• MSRI Summer School Algebraic Theory of Differential and Difference Equations, Model Theory and their Applications (Berkeley, July 2022)

• Online Workshop in Memory of Ray Hoobler (April, 2021)

• Workshop on Differential Galois Theory and Differential Algebraic Groups (Toronto, July 2017)

• Special Session on the Computational theory of differential and difference equations at MACIS2015 (Berlin, November 2015) 

• DART VI and International Summer School on Mathematics Mechanization (Beijing, August 2015)

• Special Session on Computational Differential and Difference Algebra at ACA 2015 (Kalamata, July 2015)

• Workshop Differential Algebra and Galois Theory (Aachen, September 2014)